IMC 2007 Q9
9. A male punky fish has 9 stripes and a female punky fish has 8 stripes. I count 86 stripes on the fish in my tank. What is the ratio of male fish to female fish?
- A 2 : 3
- B 3 : 2
- C 4 : 1
- D 4 : 7
- E 7 : 4
Intermediate Mathematical Challenge 2007, Question 9. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: B 3 : 2
If there are \(f\) females and \(m\) males then \(86 = 8f + 9m = 8(f + m) + m\). Now 86 = 8 × 10 + 6 = 8 × 9 + 14 = 8 × 8 + 22…. Only the first of these is feasible (because \(f + m \geqslant m\)). So \(m = 6\) and \(f = 4\).
Solution © UK Mathematics Trust, from the IMC 2007 solutions.